Minimal surface scaffold designs for tissue engineering

Modeling the temperature dependent ultimate tensile strength of fiber/polymer composites considering fiber agglomeration

Parametric design and evaluation of TPMS-like cellular solids

Numerical analysis of the influence of triply periodic minimal surface structures morphometry on the mechanical response

Colloidal dynamics and elasticity of dense wax particle suspensions over a wide range of volume fractions when tuning the softness by temperature

Porous scaffold design by solid T-splines and triply periodic minimal surfaces

This paper studies the determination of rigorous upper and lower bounds on the effective transport and elastic moduli of a transversely isotropic fiber-reinforced composite derived by Silnutzer and by Milton. The third-order Silnutzer bounds on the transverse conductivity σe, the transverse bulk modulus ke, and the axial shear modulus μe, depend upon the microstructure through a three-point correlation function of the medium. The fourth-order Milton bounds on σe and μe depend not only upon three-point information but upon the next level of information, i.e., a four-point correlation function. The aforementioned microstructure-sensitive bounds are computed, using methods and results of statistical mechanics, for the model of aligned, infinitely long, equisized, circular cylinders which are randomly distributed throughout a matrix, for fiber volume fractions up to 65 percent. For a wide range of volume fractions and phase property values, the Silnutzer bounds significantly improve upon corresponding second-order bounds due to Hill and to Hashin; the Milton bounds, moreover, are narrower than the third-order Silnutzer bounds. When the cylinders are perfectly conducting or perfectly rigid, it is shown that Milton’s lower bound on σe or μe provides an excellent estimate of these effective parameters for the wide range of volume fractions studied here. This conclusion is supported by computer-simulation results for σe and by experimental data for a graphite-plastic composite.

The present work investigates the influence of material phases and their volume fractions on the elastic behavior of triply periodic minimal surface (TPMS) scaffolds for the potential modeling of bone scaffolds. A graphical tool using TPMS functions, namely Schwarz-D (diamond), gyroid, and modified gyroid, was developed and used to design and additively manufacture 3D multiphase scaffold models. A PolyJet, UV-cured 3D-printer system was used to fabricate the various TPMS scaffold models using three polymer materials with high, medium, and low stiffness properties. All TPMS models had the same volume fractions of the three polymer materials. Final models were printed into cylinders with a diameter of 20 mm and a height of 8 mm for mechanical testing. The models were subjected to compressive and shear testing using a dynamic mechanical analysis rheometer. All samples were tested at physiologically relevant temperature (37°C) to provide detailed structural characterizations. Microscopic imaging of 3D-printed scaffold longitudinal and cross sections revealed that additive manufacturing adequately recreated the TPMS functions, which created anisotropic materials with variable structures in the longitudinal and transverse directions. Mechanical testing showed that all three TPMS 3D-printed scaffold types exhibited significantly different shear and compressive properties (verifying anisotropic properties) despite being constructed of the same volume fractions of the three UV-printed polymer materials. The gyroid and diamond scaffolds demonstrated complex moduli values that ranged from 1.2 to 1.8 times greater than the modified gyroid scaffolds in both shear and compression. Control scaffolds printed from 100% of each of the three polymers had statistically similar mechanical properties, verifying isotropic properties.

Cell-laden, scaffold-based tissue engineering methods have been successfully utilized for the treatment of bone fractures and diseases, caused by factors such as trauma, tumors, congenital anomalies, and aging. In such methods, the rate of scaffold biodegradation, transport of nutrients and growth factors, as well as removal of cell metabolic wastes at the site of injury are critical fluid-dynamics factors, affecting cell proliferation and ultimately tissue regeneration. Therefore, there is a critical need to identify the underlying material transport mechanisms and factors associated with cell-seeded, scaffold-based bone tissue engineering. The overarching goal of this study is to contribute to patient-specific, clinical treatment of bone pathology. The overall objective of the work is to establish computational fluid dynamics (CFD) models: (i) to identify the consequential mechanisms behind internal and external material transport through/over porous bone scaffolds designed based on the principles of triply periodic minimal surfaces (TPMS) and (ii) to identify TPMS designs with optimal geometry and flow characteristics for the treatment of bone fractures in clinical practice. In this study, advanced CFD models were established based on ten TPMS scaffold designs for (i) single-unit internal flow analysis, (ii) single-unit external flow analysis, and (iii) cubic, full-scaffold external flow analysis, where the geometry of each design was parametrically created. The influence of several design parameters, such as surface representation iteration, wall thickness, and pore size on geometry accuracy as well as computation time, was investigated in order to obtain computationally efficient and accurate CFD models. The fluid properties (such as density and dynamic viscosity) as well as the boundary conditions (such as no-slip condition, inlet flow velocity, and pressure outlet) of the CFD models were set based on clinical/research values reported in the literature, according to the fundamentals of internal and external Newtonian flow modeling. The main fluid characteristics influential in bone regeneration, including flow velocity, flow pressure, and wall shear stress (WSS), were analyzed to observe material transport internally through and externally over the TPMS scaffold designs. Regarding the single-unit internal flow analysis, it was observed that P.W. Hybrid and Neovius designs had the highest level of not only flow pressure but also WSS. This can be attributed to their relatively flat surfaces when compared to the rest of the TPMS designs. Schwarz primitive (P) appeared to have the lowest level of flow pressure and WSS (desirable for development of bone tissues) due to its relatively open channels allowing for more effortless fluid transport. An analysis of streamline velocity exhibited an increase in velocity togther with a depiction of potential turbulent motion along the curved sections of the TPMS designs. Regarding the single-unit external flow analysis, it was observed that Neovius and Diamond yielded the highest level of flow pressure and WSS, respectively, while Schwarz primitive (P) similarly had a relatively low level of flow pressure and WSS suitable for bone regeneration. Besides, pressure buildup was observed within the inner channels of almost all the TPMS designs due to flow resistance and the intrinsic interaction between the fluid flow and the scaffold walls. Regarding the cubic (full-scaffold) external flow analysis, the Diamond and Schwarz gyroid (G) designs appeared to have a relatively high level of both flow pressure and WSS, while Schwarz primitive (P) similarly yielded a low level of flow pressure and WSS. Overall, the outcomes of this study pave the way for optimal design and fabrication of complex, bone-like tissues with desired material transport properties for cell-laden, scaffold-based treatment of bone fractures.

We performed direct numerical simulations of non-Brownian sedimenting particles, using a smooth profile method over a wide range of volume fractions from 0.01 to 0.5. We found that hydrodynamic velocity fluctuations scale as ϕ1/2, both parallel and perpendicular to gravity at low volume fractions (ϕ ≤ 0.04) due to anisotropic microstructure and decay with further increase in ϕ because of many body hydrodynamic interactions. Unlike velocity fluctuations, vertical relaxation times scale as ϕ−1/2 for the full range of volume fractions, whereas horizontal relaxation times decrease as ϕ−1/2 at low volume fractions, remain unchanged and then decrease sharply at high volume fractions. Similarly, horizontal and vertical diffusion coefficients increase as ϕ1/2 at low volume fractions. Moreover, vertical diffusion decays with further increase in ϕ, whereas horizontal diffusion remains unchanged and then decreases. The microstructure analysis of the suspension showed that at low volume fractions the anisotropic microstructure determines the transport properties and at ϕ > 0.12 many body interactions govern the system properties, whereas a cross-over exists in between these two regimes.

The concept of “functional tissue engineering” proposes that biomaterial scaffolds should be developed with mechanical properties that approximate those of native tissues. This can present a challenge as soft tissues exhibit at a minimum nonlinear elastic properties. The question becomes how to computationally estimate effective properties for scaffolds made from nonlinear materials and whether these nonlinear effective properties can be estimated from linear homogenization analysis. In this chapter, contact analyses are performed for both Triply Minimal Periodic Surface (TPMS) and P Schwartz architecture for 1×1×1 to 5×5×5 repeated unit cells for both linear and nonlinear (Neo-Hookean) base materials. These are compared to linear homogenization analyses for the same scaffold architecture. Results show that nonlinear effective properties show the same trend of decreasing material coefficients as linear effective properties as scaffold porosity increases. Furthermore, linear homogenization resulted bounded both linear and nonlinear multi-cell contact analyses. The results provide an initial insight into the behavior of porous scaffolds made from nonlinear materials as well as suggesting that linear homogenization estimates can be used as initial bounds for nonlinear effective properties of porous scaffolds.

Triply Periodic Minimal Surfaces (TPMS), a class of intricate mathematical surfaces, have emerged as a promising framework for scaffold design due to their ability to replicate the complex geometries found in biological structures. Four TPMS structures, the Schwarz Diamond (D), Schwarz Primitive (P), Gyroid, and IWP (I-wrapped package) were designed for both uniform and graded density and additively manufactured through Stereolithography based additive manufacturing (AM) techniques using biomedical graded material. Two different mechanical tests, tensile and compression tests were examined on the TPMS structure to study their mechanical properties. The results showed that Schwarz D and IWP TPMS show greater tensile strength for both uniform and graded structures with 18.22 MPa and 14.41 MPa in uniform structures and 9.89 MPa and 9.23 MPa in graded structures of Schwarz D and IWP respectively. Uniform TPMSs show overall tensile strength over the graded TPMS. Compressive properties also show that Schwarz D and IWP TPMS have greater compressive strength in both uniform and graded TPMS, where overall graded structures show better strength over the uniform. Graded Schwarz D observed to have 100.68 MPa, and IWP TPMS has 99.57 MPa, and uniform Schwarz D has 33.94 MPa, whereas IWP TPMS shows 31.82 MPa compressive strength. Results reinforce the structure’s suitability for scaffold applications, particularly in contexts demanding robust mechanical integrity. The application of SLA AM with biomedical-graded material strengthens the viability in areas like tissue engineering and regenerative medicine.

Introduction: Triply periodic minimal surface (TPMS) is widely used in the design of bone scaffolds due to its structural advantages. However, the current approach to designing bone scaffolds using TPMS structures is limited to a forward process from microstructure to mechanical properties. Developing an inverse bone scaffold design method based on the mechanical properties of bone structures is crucial.Methods: Using the machine learning and genetic algorithm, a new inverse design model was proposed in this research. The anisotropy of bone was matched by changing the number of cells in different directions. The finite element (FE) method was used to calculate the TPMS configuration and generate a back propagation neural network (BPNN) data set. Neural networks were used to establish the relationship between microstructural parameters and the elastic matrix of bone. This relationship was then used with regenerative genetic algorithm (RGA) in inverse design.Results: The accuracy of the BPNN-RGA model was confirmed by comparing the elasticity matrix of the inverse-designed structure with that of the actual bone. The results indicated that the average error was below 3.00% for three mechanical performance parameters as design targets, and approximately 5.00% for six design targets.Discussion: The present study demonstrated the potential of combining machine learning with traditional optimization method to inversely design anisotropic TPMS bone scaffolds with target mechanical properties. The BPNN-RGA model achieves higher design efficiency, compared to traditional optimization methods. The entire design process is easily controlled.

A systematic study of the rheological properties of solutions of non-motile microalgae (Chlorella vulgaris CCAP 211-19) in a wide range of volume fractions is presented. As the volume fraction is gradually increased, several rheological regimes are observed. At low volume fractions (but yet beyond the Einstein diluted limit), the sus- pensions display a Newtonian rheological behaviour and the volume fraction dependence of the viscosity can be well described by the Quemada model (Quemada, Eur Phys J Appl Phys 1:119-127, 1997). For intermediate values of the volume fraction, a shear thinning behaviour is observed and the volume fraction dependence of the viscosity can

Simultaneous optimization of stiffness, permeability, and surface area in metallic bone scaffolds

Equilibrium molecular dynamics simulations are conducted to investigate heat transport in aqueous suspensions of alumina nanoparticles. The thermal conductivity of the suspension, calculated by the Green-Kubo relations, is studied for a wide range of volume fractions, particle sizes, and temperatures. The particle volume fraction is varied in the range of 1-9% and the particle size range of concern is 1-9 nm. The temperature varies between 300 and 370 K. The radial distribution function and the radial density profiles are utilized to estimate the thickness of the ordered base-fluid nanolayer adsorbed on the particle surface. Emphasis is placed on elucidating the relationship between the thermal conductivity enhancement and the nanolayer thickness. Results show that the effective thermal conductivity increases near-linearly as a function of volume fraction, whereas the slope of this function decreases with an increase in particle size. The nanolayer thickness is independent of the particle volume fraction. The effect of particle size on thermal conductivity is studied for a volume fraction of 5%, temperature of 300 K, and pressure of 1 atm. The nanolayer thickness remains almost constant with an increase in particle size. However, both effective thermal conductivity, and nanolayer thickness normalized with particle diameter decreases sharply with increasing particle size and attains an asymptotic value at particle diameter ~ 150 nm. The effect of temperature on the effective thermal conductivity is studied for a particle size of 3 nm and volume fraction of 5%. The thermal conductivity decreases steadily with increasing temperature, whereas the nanolayer thickness remains nearly constant. For particle sizes less than 10 nm, the enhancement in thermal conductivity is significantly greater than the predictions of existing theoretical models. A strong correlation between nanolayer properties and enhanced thermal conductivity of fully dispersed nanoparticle suspensions can be deduced from the results.